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You are shown a set of four cards placed on a table, each of which has a number on one side and a colored patch on the other side. The visible faces of the cards show 3, 8, red and brown. Which card(s) must you turn over in order to test the truth of the proposition that if a card shows an even number on one face, then its opposite face is red?

@GabbyD123 ; why would there be a red side under the card with number 3?

The rule we are trying to verify is that if there is and even number on a side of the card, the other side will be red. 3 is not an even number, turning it won't prove anything in regard of our hypothesis.

@Zelarith Turning over the cards with even numbers or red only would mean nothing without something to match it against.

For example, if we turned over the eight and there is red and we turned over the red and there is a six, we would draw the conclusion that even numbers are always under red cards and vice versa. But what if there was a 2 under the brown card but we never turned it over? Then our conclusion would be false and we'd feel like idiots if a three-year-old walked up to one of the brown cards, turned it over and said "Hey, look! That's a two! I know my numbers! YAAAAAY!!!". Therefore, we'd need to turn the eight to confirm that an even number has red under it and turn the three to confirm that ONLY even numbers have red under them.

It's basically the same thing you said in your previous comment.
[You must turn the "8" to verify that it is red on the other side, but also the brown card to ensure the number on its other face isn't even.][/quote]

I still disagree, if you turn the 3 and there is red under it, it doesn't proove the proposition"[quote tartle]if a card shows an even number on one face, then its opposite face is red[/quote]" to be wrong.

It would proove the proposition "ONLY cards with an even number on one face have its opposite face red" to be wrong, wich is why the backface of that 3 is of no consequence for our proposition, and why I say it'ss pointless to turn it.